How many arms to support a 200lb floating desk?

Hi all, I’m a newbie building a floating desk. The desk is 118” long with a 1” birch surface covered in 3/8” glass. The top’s total weight is approximately 200lbs and should support another 200lbs in daily use. I was wondering if there is any math behind figuring out how many arms to install under the desk for support. I have 7 studs to use with the leftmost four being under a window (does this matter as far as the load support?). The desk itself is 30” deep and, if possible, I’d like the arms to be no deeper than 20”.

I was hoping to go with four arms, two at the ends and two throughout the middle. Would 20” deep arms support this load? Is there a good resource for information on the math or techniques for supporting such a deep desk?

I think it is relevant to tell us about the design of these arms. Are they braced? Is so, how low on the wall does the brace connect and how far out on the arm does the brace connect? If the arm comes out 20 inches and the brace connects to the wall 20 inches below the bottom of the top and connects to the end of the arm, you can support a lot more than if the brace connects at a higher level on the wall and/or a shorter distance out on the arm.

Let me suggest that this is a issue you can test. Install a single arm and suspend some weight from it. That should tell you a lot about what the arm can support.

Let me also suggest that there is no sin in making the support stronger than needed (other than visual appearances). I would probably put an arm on each stud.

Thanks cracknpop, those look like much better supports than what I would have built myself. The bottom of the desk will be around 30” off the ground, so I don’t need anything sexy since the supports will be mostly invisible. These look strong enough that I imagine I can get away with one on each side and one in the middle for support.

Richgreer, the brackets suggested by cracknpop are 21.5” x 14.25”. I think I’d rather go with the 19.5” x 13” brackets as they would be installed into 3/4” plywood supports to raise the bracket over the cleat. What do you think?